Question Rewrite the problem statement: Find the frequency distribution and construct a histogram for the hottest recorded temperatures (in °F) across 16 North American cities.
$92.5-96.5$ : $\square$ $96.5-100.5$ : $\square$ $100.5-104.5$ : $\square$ $104.5-108.5$ : $\square$ $108.5-112.5$ : $\square$

Studdy Solution

STEP 1

Assumptions
1. The temperatures are given in degrees Fahrenheit.
2. The class width for the grouped frequency distribution is 4 degrees Fahrenheit.
3. The temperature ranges for the classes do not overlap and are continuous.
4. The frequency is the count of the number of cities that fall within each temperature range.

STEP 2

Sort the given temperatures in ascending order to make it easier to count the frequency for each class.
The sorted temperatures are: $93, 95, 97, 97, 98, 99, 101, 102, 103, 104, 105, 106, 107, 111, 111, 112$

STEP 3

Count the number of temperatures that fall within the first class range $92.5-96.5$ .
The temperatures that fall within this range are: $93, 95$ .

STEP 4

Count the number of temperatures that fall within the second class range $96.5-100.5$ .
The temperatures that fall within this range are: $97, 97, 98, 99$ .

STEP 5

Count the number of temperatures that fall within the third class range $100.5-104.5$ .
The temperatures that fall within this range are: $101, 102, 103, 104$ .

STEP 6

Count the number of temperatures that fall within the fourth class range $104.5-108.5$ .
The temperatures that fall within this range are: $105, 106, 107$ .

STEP 7

Count the number of temperatures that fall within the fifth class range $108.5-112.5$ .
The temperatures that fall within this range are: $111, 111, 112$ .

STEP 8

Complete the grouped frequency distribution table with the counted frequencies.
\begin{tabular}{|cc|} \hline \begin{tabular}{c} Temperatures \\ $\left(\right.$ in $\left.^{\circ} \mathrm{F}\right)$ \end{tabular} & Frequency \\ \hline $92.5-96.5$ & 2 \\ $96.5-100.5$ & 4 \\ $100.5-104.5$ & 4 \\ $104.5-108.5$ & 3 \\ $108.5-112.5$ & 3 \\ \hline \end{tabular}

STEP 9

To construct a histogram, we will use the temperature ranges as the horizontal axis (x-axis) and the frequency as the vertical axis (y-axis).

STEP 10

For each class range, draw a bar whose height corresponds to the frequency of that class.

STEP 11

Make sure the bars are adjacent to each other with no gaps because the data is continuous.

STEP 12

Label the x-axis with the temperature ranges and the y-axis with the frequency.

STEP 13

Title the histogram appropriately, for example, "Histogram of Hottest Recorded Temperatures in North American Cities."

STEP 14

Check that all bars are correctly drawn and that the histogram accurately represents the grouped frequency distribution.
The histogram should now be complete, with each bar representing the frequency of temperatures within the specified ranges.

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Studdy Solution

STEP 1

STEP 2

Sort the given temperatures in ascending order to make it easier to count the frequency for each class.
The sorted temperatures are: $93, 95, 97, 97, 98, 99, 101, 102, 103, 104, 105, 106, 107, 111, 111, 112$

STEP 3

Count the number of temperatures that fall within the first class range $92.5-96.5$ .
The temperatures that fall within this range are: $93, 95$ .

STEP 4

Count the number of temperatures that fall within the second class range $96.5-100.5$ .
The temperatures that fall within this range are: $97, 97, 98, 99$ .

STEP 5

Count the number of temperatures that fall within the third class range $100.5-104.5$ .
The temperatures that fall within this range are: $101, 102, 103, 104$ .

STEP 6

Count the number of temperatures that fall within the fourth class range $104.5-108.5$ .
The temperatures that fall within this range are: $105, 106, 107$ .

STEP 7

Count the number of temperatures that fall within the fifth class range $108.5-112.5$ .
The temperatures that fall within this range are: $111, 111, 112$ .

STEP 8

STEP 9

To construct a histogram, we will use the temperature ranges as the horizontal axis (x-axis) and the frequency as the vertical axis (y-axis).

STEP 10

For each class range, draw a bar whose height corresponds to the frequency of that class.

STEP 11

Make sure the bars are adjacent to each other with no gaps because the data is continuous.

STEP 12

Label the x-axis with the temperature ranges and the y-axis with the frequency.

STEP 13

Title the histogram appropriately, for example, "Histogram of Hottest Recorded Temperatures in North American Cities."

STEP 14

Check that all bars are correctly drawn and that the histogram accurately represents the grouped frequency distribution.
The histogram should now be complete, with each bar representing the frequency of temperatures within the specified ranges.

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Studdy Solution

STEP 1

STEP 2

STEP 3

Count the number of temperatures that fall within the first class range 92.5−96.592.5-96.592.5−96.5.The temperatures that fall within this range are: 93,9593, 9593,95.

STEP 4

Count the number of temperatures that fall within the second class range 96.5−100.596.5-100.596.5−100.5.The temperatures that fall within this range are: 97,97,98,9997, 97, 98, 9997,97,98,99.

STEP 5

Count the number of temperatures that fall within the third class range 100.5−104.5100.5-104.5100.5−104.5.The temperatures that fall within this range are: 101,102,103,104101, 102, 103, 104101,102,103,104.

STEP 6

Count the number of temperatures that fall within the fourth class range 104.5−108.5104.5-108.5104.5−108.5.The temperatures that fall within this range are: 105,106,107105, 106, 107105,106,107.

STEP 7

Count the number of temperatures that fall within the fifth class range 108.5−112.5108.5-112.5108.5−112.5.The temperatures that fall within this range are: 111,111,112111, 111, 112111,111,112.

STEP 8

STEP 9

To construct a histogram, we will use the temperature ranges as the horizontal axis (x-axis) and the frequency as the vertical axis (y-axis).

STEP 10

For each class range, draw a bar whose height corresponds to the frequency of that class.

STEP 11

Make sure the bars are adjacent to each other with no gaps because the data is continuous.

STEP 12

Label the x-axis with the temperature ranges and the y-axis with the frequency.

STEP 13

Title the histogram appropriately, for example, "Histogram of Hottest Recorded Temperatures in North American Cities."

STEP 14

Check that all bars are correctly drawn and that the histogram accurately represents the grouped frequency distribution.The histogram should now be complete, with each bar representing the frequency of temperatures within the specified ranges.

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Count the number of temperatures that fall within the first class range $92.5-96.5$ .
The temperatures that fall within this range are: $93, 95$ .

Count the number of temperatures that fall within the second class range $96.5-100.5$ .
The temperatures that fall within this range are: $97, 97, 98, 99$ .

Count the number of temperatures that fall within the third class range $100.5-104.5$ .
The temperatures that fall within this range are: $101, 102, 103, 104$ .

Count the number of temperatures that fall within the fourth class range $104.5-108.5$ .
The temperatures that fall within this range are: $105, 106, 107$ .

Count the number of temperatures that fall within the fifth class range $108.5-112.5$ .
The temperatures that fall within this range are: $111, 111, 112$ .

Check that all bars are correctly drawn and that the histogram accurately represents the grouped frequency distribution.
The histogram should now be complete, with each bar representing the frequency of temperatures within the specified ranges.